# scipy.special.roots_sh_chebyu¶

scipy.special.roots_sh_chebyu(n, mu=False)[source]

Gauss-Chebyshev (second kind, shifted) quadrature.

Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the n-th degree shifted Chebyshev polynomial of the second kind, $$U_n(x)$$. These sample points and weights correctly integrate polynomials of degree $$2n - 1$$ or less over the interval $$[0, 1]$$ with weight function $$f(x) = \sqrt{x - x^2}$$.

Parameters
nint

quadrature order

mubool, optional

If True, return the sum of the weights, optional.

Returns
xndarray

Sample points

wndarray

Weights

mufloat

Sum of the weights

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